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Solving Multi-Step Equations

ALGEBRA 1 LESSON 2-3

(For help, go to Lessons 1-2 and 1-7.)

Simplify each expression. 1. 2n 3n 2. 4 3b

2 5b 3. 9(w 5) 4. 10(b 12) 5. 3(x

4) 6. 5(6 w) Evaluate each expression. 7. 28

a 4a for a 5 8. 8 x 7x for x 3 9. (8n

1)3 for n 2 10. (17 3y) for y 6

2-3

Solving Multi-Step Equations

ALGEBRA 1 LESSON 2-3

Solutions

1. 2n 3n (2 3)n 1n n 2. 4 3b 2

5b (3 5)b (4 2) 8b 2 3. 9(w 5)

9w 9(5) 9w 45 4. 10(b 12) 10b

(10)(12) 10b 120 5. 3(x 4) 3(x)

3(4) 3x 12 6. 5(6 w) 5(6) 5w 30

5w 7. 28 a 4a for a 5 28 5 4(5) 28

5 20 23 20 43 8. 8 x 7x for x

3 8 (3) 7(3) 8 (3) 21 5 21

26 9. (8n 1)3 for n 2 (8(2) 1)3 (16

1)3 (15)3 45 10. (17 3y) for y 6

(17 3(6)) (17 18) 35

2-3

Solving Multi-Step Equations

ALGEBRA 1 LESSON 2-3

Solve 3a 6 a 90

4a 6 90 Combine like terms.

4a 6 6 90 6 Subtract 6 from each side.

4a 84 Simplify.

2-3

Solving Multi-Step Equations

ALGEBRA 1 LESSON 2-3

You need to build a rectangular pen in your back

yard for your dog. One side of the pen will be

against the house. Two sides of the pen have a

length of x ft and the width will be 25 ft. What

is the greatest length the pen can be if you have

63 ft of fencing?

2-3

Solving Multi-Step Equations

ALGEBRA 1 LESSON 2-3

(continued)

x 25 x 63

2x 38 Simplify.

x 19

The pen can be 19 ft long.

2-3

Solving Multi-Step Equations

ALGEBRA 1 LESSON 2-3

Solve 2(x 3) 8

2x 6 8 Use the Distributive Property.

2x 6 6 8 6 Add 6 to each side.

2x 14 Simplify.

x 7 Simplify.

2-3

Solving Multi-Step Equations

ALGEBRA 1 LESSON 2-3

Solve 17

3x2

x5

x 10 Simplify.

2-3

Solving Multi-Step Equations

ALGEBRA 1 LESSON 2-3

Solve 17

3x2

x5

15x 2x 170 Multiply.

17x 170 Combine like terms.

x 10 Simplify.

2-3

Solving Multi-Step Equations

ALGEBRA 1 LESSON 2-3

Solve 0.6a 18.65 22.85.

100(0.6a 18.65) 100(22.85) The greatest of

decimal places is two places. Multiply each side

by 100.

100(0.6a) 100(18.65) 100(22.85) Use the

Distributive Property.

60a 1865 2285 Simplify.

60a 1865 1865 2285 1865 Subtract 1865

from each side.

60a 420 Simplify.

2-3

Solving Multi-Step Equations

ALGEBRA 1 LESSON 2-3

Solve each equation. 1. 4a 3 a 24 2.

3(x 5) 66 3. 7 4. 0.05x

24.65 27.5

7

17

n3

n4

12

57

2-3

Equations with Variables on Both Sides

ALGEBRA 1 LESSON 2-4

(For help, go to Lessons 1-7 and 2-3.)

Simplify. 1. 6x 2x 2. 2x 6x 3. 5x

5x 4. 5x 5x Solve each equation. 5. 4x 3

5 6. x 7 12 7. 2t 8t 1 43 8. 0

7n 4 5n

2-4

Equations with Variables on Both Sides

ALGEBRA 1 LESSON 2-4

Solutions

1. 6x 2x (6 2)x 4x 2. 2x 6x (2 6)x

4x 3. 5x 5x (5 5)x 0x 0 4. 5x

5x (5 5)x 0x 0 5. 4x 3 5 6. x

7 12 4x 8 x 5 x 2 x 5 7. 2t

8t 1 43 8. 0 7n 4 5n 6t

1 43 0 12n 4

6t 42 12n 4 t 7 n

1 3

2-4

Equations with Variables on Both Sides

ALGEBRA 1 LESSON 2-4

The measure of an angle is (5x 3). Its

vertical angle has a measure of (2x 12). Find

the value of x.

5x 3 2x 12 Vertical angles are congruent.

2-4

Equations with Variables on Both Sides

ALGEBRA 1 LESSON 2-4

You can buy a skateboard for 60 from a friend

and rent the safety equipment for 1.50 per hour.

Or you can rent all items you need for 5.50 per

hour. How many hours must you use a skateboard to

justify buying your friends skateboard?

2-4

Equations with Variables on Both Sides

ALGEBRA 1 LESSON 2-4

(continued)

60 1.5h 5.5h

You must use your skateboard for more than 15

hours to justify buying the skateboard.

2-4

Equations with Variables on Both Sides

ALGEBRA 1 LESSON 2-4

Solve each equation.

a. 6z 8 z 10 7z

6z 8 z 10 7z

6z 8 6z 10 Combine like terms.

6z 8 6z 6z 10 6z Add 6z to each side.

8 10 Not true for any value of z!

This equation has no solution

b. 4 4y 2(2y 2)

4 4y 2(2y 2)

4 4y 4y 4 Use the Distributive Property.

4 4y 4y 4y 4 4y Add 4y to each side.

4 4 Always true!

The equation is true for every value of y, so

the equation is an identity.

2-4

Equations with Variables on Both Sides

ALGEBRA 1 LESSON 2-4

Solve each equation. 1. 3 2t 7t 4 2. 4n

2(n 1) 3(n 1) 3. 3(1 2x) 4

6x 4. You work for a delivery service. With Plan

A, you can earn 5 per hour plus .75 per

delivery. With Plan B, you can earn 7 per hour

plus .25 per delivery. How many deliveries must

you make per hour with Plan A to earn as much as

with Plan B?

1

no solution

4 deliveries

2-4

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